Critical flow orifice/Venturi

From Equation 2.12, it is clear that for a given set of conditions, the flow through the orifice/Venturi will increase for a decrease in absolute pressure ratio P2/P1, xmtil a linear velocity in the throat reaches the velocity of soimd. The value of P2/P1 for which the acoustic flow is just attained is called the critical pressure ratio r, and flow at such a condition is called critical or choked flow. Under choked flow situations, the flow through the orifice depends only on the upstream pressure. 

Critical flow through the orifice/Venturi can be expressed as [3]... 

Accuracy Square-edged orifices and venturi tubes have been so extensively studied and standardized that reproducibihties within 1 to 2 percent can be expected between standard meters when new and clean. This is therefore the order of reliabihty to be had, if one assumes (1) accurate measurement of meter differenfial, (2) selection of the coefficient of discharge from recommended published literature, (3) accurate knowledge of fluid density, (4) accurate measurement of critical meter dimensions, (5) smooth upstream face of orifice, and (6) proper location of the meter with respect to other flow-disturbing elements in the system. Care must also be taken to avoid even sh t corrosion or fouliug during use. 

These conditions are similar to flow through orifices, nozzles, and venturi tubes. Flow through nozzles and venturi devices is limited by the critical pressure ratio, r,. = downstream pressure/upstream pressure at sonic conditions (see Figure 2-38C). 

Figure 2-38C. Critical Pressure Ratio, r, for compressible flow through nozzles and venturi tubes. By permission, Crane Co., Technical Paper 410, 1957. Also see 1976 edition. See note at Figure 2-18 explaining details of data source for chart. Note P = psia p= ratio of small-to-large diameter in orifices and nozzles, and contractions or enlargements in pipes.

The bnttons at the end of the lines in Figure 5.23 for the nozzle and venturi correspond to critical (choked) flow. Althongh there are no buttons shown on the lines for the orifice, choked flow does occnr in orifices as well. However, the choked flow is not as reproducible for orifices because of the variable effects of the vena contracta. 

Lakshmana Rao, N.S. Shridharan, K. 1972. Orifice losses for laminar approach flow. ASCE Journal of Hydraulics Division, Vol.98, No.ll, (November), pp. 2015-2034 Lakshmana Rao, N.S., Srhidharan, K. Alvi, S.H. (1977). Critical Reynolds Number for orifice and nozzle flows in pipes. Journal of Hydraulic Research, International Association for Hydraulic Research, Vol. 15, No. 2, pp. 167-178 Ma, T. W. (1987). Stability, rheology and flaw in pipes, fittings and venturi meters of concentrated non-Newtonian suspensions. Unpublished PhD thesis. University of Illinois, Chicago... 

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See also in sourсe #XX -- [ ]

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